全平面上(p,q)级随机Dirichlet级数的值分布

On the Distribution of Random Dirichlet Series with (p,q) Orders in the Whole Plane

根据全平面上(p,q)级随机Dirichlet级数的定义,通过把全平面上的随机Dirichlet级数映射到单位圆上的随机Dirichlet级数,应用推广的Nevanlinna第二基本定理,证明了全平面上(p,q)级随机Dirichlet级数在一定条件下几乎必然以每条水平直线为无例外小函数的(p,q)级强Borel线,该结论丰富了Dirichlet级数的成果,具有一定的理论意义.

In this paper,the random Dirichlet series on the whole plane is mapped to the random Dirichlet series on the unit circle by the difinition of random Dirichlet series with（ p,q） orders on the whole plane. Using the generalized second Nevanlinna basic theorem,we prove that the random Dirichlet series with（ p,q） orders almost surely take every horizontal line as a strong Borel line and without exceptional little functions. This result enriches the theory about Dirichlet series and has a certain theoretical signification.